statistics AND probability • chance
10A
The language of chance
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An event is a result or outcome that may occur.
When rating the chance of a certain event occurring, we use words like certain, likely, even
chance, unlikely and impossible.
The probability of an event occurring is given a value between 0 and 1 inclusive.
If an event it certain, like an Australian Cricket team being named this summer, the
probability of it occurring is 1.
If an event is impossible, such as Christmas Day falling in June this year, the probability of it
occurring is 0.
If an event has an even chance of occurring, such as the probability of tossing a head with a
fair coin, the probability of it occurring is 0.5. Probabilities can be written as fractions and
1
percentages. For example, 0.5 = 2 = 50%.
The probability scale, below, associates important words used in describing probability with
their approximate corresponding numerical values.
Highly
unlikely
0.1
0.2
0.3
0.4
Better than
even chance
0.5
Highly
likely
Likely
Even
chance
Less than
even chance
Very
unlikely
Impossible
0
Unlikely
0.6
Very
likely
0.7
0.8
Certain
0.9
1.0
Worked Example 1
For each of the given statements, specify whether the chance of the following events occurring is
certain, likely, even chance, unlikely or impossible.
a You will compete in the next Olympics.
b Every student in Year 7 will obtain 100% in their next mathematics test.
c Each person in your class has been to the zoo.
d You flip a coin and Tails comes up.
e March is followed by April.
Think
Write
Read the given statement and associate
the chance of the event occurring with
one of the given words from the list.
Provide reasons.
2 Answer the question.
b Repeat steps 1 and 2 of part a.
a The chance of a person competing in the next
c
Repeat steps 1 and 2 of part a.
c
d Repeat steps 1 and 2 of part a.
d
e Repeat steps 1 and 2 of part a.
e
a
1
Olympics is very small; however, it could happen.
b
It is unlikely that this event will occur.
Due to each student having different capabilities and
the number of students involved, this situation could
never happen. It is impossible for this event to occur.
The chance that each student in your class has been
to the zoo, either with their family or primary school,
is very probable. However, there may be a few
students who missed out.
It is likely this event will occur.
When you flip a coin there are only two possibilities,
a Head or a Tail. So there is a 50% chance of Tails
coming up.
There is an even chance this event will occur.
This is a true statement. April always follows the
month of March.
It is certain this event will occur.
Chapter 10 Probability
357
statistics AND probability • chance
Worked Example 2
Assign a number between and including 0 and 1 to represent the estimated probability of the
following events, depending on how likely they are.
a One of two evenly matched tennis players will win the next game.
b You will guess the correct answer on a multiple choice question with four options.
c Rolling a fair die and obtaining a number less than 6.
Think
a
b
c
1
Write
2
Express the answer as a decimal.
1
Determine the likelihood of an event
occurring, with reasoning.
does not have an advantage over the other.
Therefore, they each have an equal chance of
winning the next game.
The probability that one player wins the game is
1
or 0.5.
2
2
Express the answer as a decimal.
1
Determine the likelihood of an event
occurring, with reasoning.
2
a Since the two players are evenly matched, one
Determine the likelihood of an event
occurring, with reasoning.
b When guessing an answer on a multiple choice
question with 4 options, 1 out of the 4 possibilities
will be correct. One out of 4 may be expressed as
a fraction.
The probability of guessing the correct answer is
1
or 0.25.
4
c When rolling a die there are six possibilities.
They are 1, 2, 3, 4, 5, 6. A number less than 6
includes 1, 2, 3, 4, 5. Therefore, five out of the six
possibilities may be rolled. Five out of six may be
expressed as a fraction.
Express the answer as a decimal,
correct to 2 decimal places.
The probability of obtaining a number less than
six is 65 or approximately 0.83.
remember
1. An event is a result that may occur.
2. Probability is the chance of a particular event (result) occurring.
3. The probability of an event occurring ranges from and includes 0 (impossible) to 1
(certain).
4. A probability scale associates important words used in describing probabilities with
their approximate corresponding numerical values.
Highly
unlikely
358
0
0.1
0.2
Maths Quest 7 for the Australian Curriculum
0.3
0.4
Better than
even chance
0.5
Highly
likely
Likely
Even
chance
Less than
even chance
Very
unlikely
Impossible
Unlikely
0.6
Very
likely
0.7
0.8
Certain
0.9
1.0